Surface waves in thermocapillary flow–revisited

Abstract

Following theoretical predictions [1,2] thermocapillary layers can exhibit instabilities called “hydrothermal waves” (HTWs) and “surface waves” (SWs) at sufficiently large Marangoni numbers. Only two experiments on thermocapillary layers in annular gaps describe SWs until now whereas HTWs have been found and investigated many times. We review and complement the results on SWs in thermocapillary annular gaps which are in fair agreement with theory, though severe differences between experimental and theoretical boundary conditions exist. Surface waves exhibit a considerably larger frequency, phase speed and surface deformation-amplitude compared to HTWs. The critical Marangoni numbers of the SWs are larger than those of the HTWs for layer depth d < 1.7 mm at which depth they cross over. SWs and HTWs are found to coexist for a certain range of liquid depths at supercritical Marangoni numbers. Surprisingly, thermocapillary instabilities of the type of SWs can exist in the liquid meniscus at the cold end-wall in an underfilled cuvette with buoyant-thermocapillary convection and they can excite standing gravity surface waves under resonance conditions. These conditions are the underfilling of the cuvette (the meniscus shape) and the temperature difference between the end-walls. Experimental evidence for this complex phenomenon is presented.